Month: May 2016

One of the scandals for my students is that the Church is a part of the Gospel. Not just the hearer of the Gospel. Not just the people who happens to pass it on. Not just a free association of like-minded believers trying to live it out.

My students want a proof that legitimizes the Church–the “Why should I bother being Catholic?” question–before listening to Her. But only the Gospel itself can legitimize the Church, and She speaks from within that Gospel. Continue reading Sermon on the Mount and the Church

More on my love affair with primes. This one is a terrific, infallible test for prime numbers:

For any prime number P

(P-1)! + 1 = x

X is divisible by P (the original prime)

I’d never heard this one before. Made me sit up in my chair when the video started rolling. Primes always pass this test, composites always fail it. The video goes on to show a small group of primes where the result is divisible by P twice. Enjoy the vid and math on.

Caesar has finally cornered Ariovistus and the Germans. The Germans attempt to delay battle to satisfy their augurs, but Caesar outmaneuvers them with a cool deception: use his auxiliaries to make it look like his camp is fully fortified while he marches his entire army against the German camp.

Ariovistus and the Germans, their hand now forced, march out against the Romans. They deploy a shield wall to turn back the infantry attack.

In the last post, on presumption and self-justification, I mentioned that the second contempt would reach its culmination in step ten. Here we are! It’s contempt for the superior.

The arrogant come to believe they are due all goods and deny the evils they do. But denial gets old and arrogant doesn’t mean stupid. In order to maintain the aura of perfection and their control over the people around them, the arrogant resort to a more deceptive form of denial: false self-accusation. Continue reading Bernard on Pride: Steps 9 and 10

A brave soul recently queried me: are Rinaldo and Orlando real or fictional heroes? The answer is “Yes.”

To be clear, Orlando Furioso is history as it should have happened. I prefer to live in a world where Charlemagne did in fact repel the combined armies of every Muslim kingdom ever with mounted heavy cavalry in full plate armor. Naturally the magical swords are real as well, and Hector’s sword is still mightily potent despite being 2000 years old. When I Google “Siege of Paris” I am puzzled to find no mention of this most momentous of battles for civilization.

Don’t get trapped fighting the last war, I often find myself thinking recently.

Fighting the last war is a great expression of ambiguous origin. It captures a simple matter of fact coupled with a warning or criticism. It is a mark of rationality to base our decisions on experience; it is a mark of irrationality to stay trapped in the past. Fighting the last war is a refusal to account for the changing circumstances in your field.

In the realm of theology, it makes you irrelevant. Fast. Trying to convince someone by the arguments of questions they are not asking and don’t care about: fighting the last war. It’s an interesting thing, being trapped by your own experience. It was valid once! But dead fish, up-stream, etc.Continue reading Fighting the Last War

The Latin game of the week in the office comes from De Bello Gallico I.40: Caesar convincing his panicking Roman legions to sack up and fight Ariovistus and his German giants. In the midst of his rhetorical genius, Caesar lays down this structurally stunning gem:

I like to toss these up on a board structurally, with indenting to show the grammatical relations. One of my least favorite things about the entire digital age is how difficult it is to do this on a screen. Sometimes the old ways are best! Since I’m not going to drive myself insane trying to replicate in MS Paint and I’m too lazy to set it up in Word and do a screen cap, you’ll have to take my word for it: it’s a cool sentence.

The apodosis (consequent) of the conditional sentence is, depending on how you want to look at it, unexpressed or borrowed from earlier in the paragraph. Basically there’s a hidden “Caesar says” introducing an indirect statement. Here’s my render: Continue reading Caesar Sunday

At the end of a bracing year of racing through Catholic doctrine with my Form III students, I always bring it back around to something as basic as possible: what is the Gospel? The amount of time I have to do this varies from year to year and is, of course, never enough. But my hyper-intelligent little skeptics need to have the Gospel proposed to them in a way other than what they see on TV or got in CCD. The simplest way to do that is to read the Sermon on the Mount (I would link to the RSV at Bibliaclerus but you’d have to internally navigate and I’m all about convenience in my hyperlinks!).

I’ve complained before that my students have the most appalling ignorance about the Sermon. It’s ironic that our cliches about Christianity come from here, and “everyone knows” that the Sermon on the Mount is the basic message of Jesus Christ. Actually, I think even that is becoming less true–we’re sliding closer to an era in which not even that much is known.

So we make our way through the text at an ambling, observational pace and I try to get them to see what the Gospel is about. Here’s the rough framework that emerges: Continue reading Sermon on the Mount

I’m moving up about fifteen weight classes when I dabble in the Riemann Hypothesis (link is to the Riemann zeta function). It’s really more a matter of what the problem represents, and my (perhaps) odd views on infinity, than it is about the zeta function itself or my ability to hack the math. I won’t be the one solving it, that’s for sure!

This video gives you a neat look at the problem although it’s a bit brief on the setup:

I thought I’d comment on why I find RH interesting.

It tickles me to no end that at the foundation of some really profound mathematics–mathematics, that realm of certainty beyond anything the physical universe allows–we have an unsolved and possibly unsolvable problem. That mystery and beauty could–and for now, in some ways, do–undergird the realm of the rational appeals to me in a highly iconoclastic way. Anselm was right and Boso was wrong! Conveniens is the more fundamental proof! (That’s a Cur Deus Homo joke. Sorry)

There’s also some low-brow humor mixed in, Pratchett-style. “Whoops, I guess everything we know about primes is wrong!” gives me a giggle. I don’t think it will turn out that way, but the idea of it delights me. Just like dying and finding out that the solar system really is geocentric would.

It’s also a really neat illustration of the difference between induction and deduction. We’ve tested trillions of candidates and they all conform to the Riemann Hypothesis…but that’s not a proof! Not in math anyway. Maybe in one of those filthy natural sciences, but Never. In. Math!